Hybrid Modelling Under Uncertainty: Effects of Model Greyness, Data Quality and Data Quantity

Abstract

Previous chapters have demonstrated how, by combining data-driven and mechanistic methods, hybrid modelling provides a cost-effective solution to modelling complex (bio)chemical reaction kinetics when the underlying mechanisms are not fully understood. However, the question of how much kinetic information to incorporate into a hybrid model (i.e., the ‘greyness’ of a hybrid model) remains to be systematically addressed. Therefore, to illustrate the effect of model greyness on accuracy and reliability, in this chapter, we built three hybrid models for predicting the kinetics of a complex biochemical system: γ-linolenic acid production via fermentation of the fungus Cunninghamella echinulata. Each hybrid model incorporated different amounts of kinetic information, representing three levels of hybrid model ‘greyness’, then embedded a Gaussian process (GP) to simulate the unknown kinetics inferred from experimental observation. Hybrid model parameter estimation is also revisited to introduce time-varying parameter regularisation to mitigate the risk of overfitting real process data with missing or uncertain measurements. Although all three hybrid models could fit well, we demonstrate how incorporating more specific kinetic information increases the risk of incorrect inductive bias, while too little renders the hybrid model prone to overfitting. By balancing the regularisation penalty weight and the amount of kinetic information provided, it is possible to build a high-fidelity hybrid model for predicting reaction system performance for new operating conditions and reactor scales. This extends the hybrid modelling theory presented in earlier chapters to meet the challenges encountered in practice.